Abstract
In this paper, M-lump and interaction between lumps and kink solitons of the $$(2+1)$$ -dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation are studied based on Hirota bilinear form. M-lump solutions are derived by taking a ‘long wave’ limit of the N-soliton solutions, and the lump–kink solutions are presented consequently. In addition, evolutions of solutions are shown by choosing certain parameters.
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